Similar Solids Lesson 23

1. Draw and label two circles that are similar. Identify their scale factor. 2. Draw two rectangles that are similar. Identify their scale factor. 3. ∆ABC is similar to ∆ XYZ. Use a proportion to solve for x x

Target: Use ratios and proportions when finding scale factors, linear ratios, area ratios and volume ratios of similar solids.

 Similar Solids: Solids with the same shape and all corresponding dimensions are proportional.

If two solids are similar then:  Their linear ratio (scale factor) is a : b.  The ratio of their areas is a 2 : b 2.  The ratio of their volumes is a 3 : b 3.

Are the cylinders similar?  Find the ratio of the radii.  Find the ratio of the heights then simplify.  Cylinders are similar if their radii and heights have the same ratio.  Cylinder A and B are similar.

Two solids have a scale factor 3 : 4. a. Find their area ratio.  Square the scale factor. 3 2 : 4 2 → 9 : 16 b. Find the volume ratio.  Raise the scale factor to the third power. 3 3 : 4 3 → 27 : 64

Two children each have an ice cream cone. The ice cream cones are similar in shape, but one is larger than the other. The cones have a scale factor of 2:5. The volume of the small cone is cm 3. Find the volume of the larger cone.  Find the volume ratio. a 3 : b 3 → 2 3 : 5 3 → 8 : 125 →  Write a proportion using the volume ratio.  Set the cross products equal. 8x =  Divide both sides by 8.88  The volume of the cone is 1, cm 3.

1. Two similar solids have an area ratio of 4² : 9². a)Identify the ratio of the linear measures. b)Identify the ratio of the volumes. c)What is the scale factor between the solids? 2. Two cylinders have a scale factor of 2 : 7. The surface area of the large cylinder is 595 square inches. Find the surface area of the smaller cylinder. Round to the nearest hundredth.

 Jeremy was told the scale factor between two solids was 4 : 7. What additional conclusions can Jeremy make about the solids?  When and where is volume used in daily life?